Quark hybrid Stars: how can we identify them? Prof. Mark Alford - - PowerPoint PPT Presentation

Quark hybrid Stars: how can we identify them?

• Prof. Mark Alford

Washington University in St. Louis

Alford, Han, Prakash, arXiv:1302.4732 Alford, Schwenzer, arXiv:1310.3524

Schematic QCD phase diagram

superconducting quark matter = color− liq

T µ

gas

QGP CFL

nuclear /supercond superfluid

compact star

non−CFL

heavy ion collider

hadronic

• M. Alford, K. Rajagopal, T. Sch¨

afer, A. Schmitt, arXiv:0709.4635 (RMP review)

• A. Schmitt, arXiv:1001.3294 (Springer Lecture Notes)

Signatures of quark matter in compact stars

Observable ← Microphysical properties

(and neutron star structure) ← Phases of dense matter

Property Nuclear phase Quark phase mass, radius eqn of state ε(p) known up to ∼ nsat unknown; many models

Signatures of quark matter in compact stars

Observable ← Microphysical properties

(and neutron star structure) ← Phases of dense matter

Property Nuclear phase Quark phase mass, radius eqn of state ε(p) known up to ∼ nsat unknown; many models spindown (spin freq, age) bulk viscosity shear viscosity Depends on phase: n p e n p e, µ n p e, Λ, Σ− n superfluid p supercond π condensate K condensate Depends on phase: unpaired CFL CFL-K 0 2SC CSL LOFF 1SC . . . cooling (temp, age) heat capacity neutrino emissivity thermal cond. glitches (superfluid, crystal) shear modulus vortex pinning energy

Nucl/Quark EoS ε(p) ⇒ Neutron star M(R)

7 8 9 10 11 12 13 14 15 Radius (km) 0.0 0.5 1.0 1.5 2.0 2.5 Mass (solar)

AP4 MS0 MS2 MS1 MPA1 ENG AP3 GM3 PAL6 GS1 PAL1 SQM1 SQM3 FSU GR P <

• c

a u s a l i t y rotation J1614-2230

J1903+0327 J1909-3744 Double NS Systems

Nucleons Nucleons+ExoticStrange Quark Matter

Recent measurement: M = 1.97 ± 0.04 M⊙

Demorest et al, Nature 467, 1081 (2010).

Can neutron stars contain quark matter cores?

Constraining QM EoS by observing M(R)

Does a 2 M⊙ star rule out quark matter cores (hybrid stars)? Lots of literature on this question, with various models of quark matter

◮ MIT Bag Model; (Alford, Braby, Paris, Reddy, nucl-th/0411016) ◮ NJL models; (Paoli, Menezes, arXiv:1009.2906) ◮ PNJL models (Blaschke et. al, arXiv:1302.6275; Orsaria et. al.;

arXiv:1212.4213)

◮ hadron-quark NLσ model (Negreiros et. al., arXiv:1006.0380) ◮ 2-loop perturbation theory (Kurkela et. al., arXiv:1006.4062) ◮ MIT bag, NJL, CDM, FCM, DSM (Burgio et. al., arXiv:1301.4060)

We need a model-independent parameterization of the quark matter EoS:

◮ framework for relating different models to each other ◮ observational constraints can be expressed in universal terms

CSS: a fairly generic QM EoS

Model-independent parameterization with Constant Speed of Sound (CSS) ε(p) = εtrans + ∆ε + c−2

QM(p − ptrans)

ε0,QM εtrans ptrans cQM

• 2

Slope = Matter Quark Matter Nuclear

Δε

Energy Density Pressure

QM EoS params: ptrans/εtrans ∆ε/εtrans c2

QM

Zdunik, Haensel, arXiv:1211.1231; Alford, Han, Prakash, arXiv:1302.4732

Hybrid star M(R)

Hybrid star branch in M(R) relation has 4 typical forms ∆ε < ∆εcrit small energy density jump at phase transition

“Connected”

R M

“Both”

M R

∆ε > ∆εcrit large energy density jump at phase transition

“Absent”

R M

“Disconnected”

M R

“Phase diagram” of hybrid star M(R)

Soft NM + CSS(c2

QM =1)

6.0 5.0 3.0

ntrans/n0

B A

2.0 4.0

C

ncausal

D

Δε/εtrans = λ-1

0.2 0.4 0.6 0.8 1 1.2

ptrans/εtrans

0.1 0.2 0.3 0.4 0.5

Schematic

trans trans ε

p ∆ε εtrans

Above the red line (∆ε > ∆εcrit), connected branch disappears ∆εcrit εtrans = 1 2 + 3 2 ptrans εtrans

(Seidov, 1971; Schaeffer, Zdunik, Haensel, 1983; Lindblom, gr-qc/9802072)

Disconnected branch exists in regions D and B.

Sensitivity to NM EoS and c2

QM c2

QM =1/3

B A

NL3

C

HLPS

D

Δε/εtrans

0.2 0.4 0.6 0.8 1 1.2

ptrans/εtrans

0.1 0.2 0.3 0.4 0.5

c2

QM =1

B A

NL3

C

HLPS

D

Δε/εtrans

0.2 0.4 0.6 0.8 1 1.2

ptrans/εtrans

0.1 0.2 0.3 0.4 0.5

• NM EoS (HLPS=soft, NL3=hard) does not make much difference.
• Higher c2

QM favors disconnected branch.

Observability of hybrid star branches

Measure length of hybrid branch by ∆M ≡ mass of heaviest hybrid star

• − Mtrans

Mtrans ∆M M R

M = Δ

• 2
• 3
• 4

0.5 0.3 0.7 10 M๏ 0.1M๏ 10 M๏ 10 M๏ 6.0 5.0 3.0

ntrans/n0

B A

2.0 4.0

C

ncausal

D

Δε/εtrans

0.2 0.4 0.6 0.8 1 1.2

ptrans/εtrans

0.1 0.2 0.3 0.4 0.5

Observability of hybrid star branches

Measure length of hybrid branch by ∆M ≡ mass of heaviest hybrid star

• − Mtrans

Mtrans ∆M M R

Soft NM + CSS(c2

QM =1)

M = Δ

• 2
• 3
• 4

0.5 0.3 0.7 10 M๏ 0.1M๏ 10 M๏ 10 M๏ 6.0 5.0 3.0

ntrans/n0

B A

2.0 4.0

C

ncausal

D

Δε/εtrans

0.2 0.4 0.6 0.8 1 1.2

ptrans/εtrans

0.1 0.2 0.3 0.4 0.5

• Connected branch is observable if ptrans is not too high

and there is no disconnected branch

• Disconnected branch is always observable

Constraints on QM EoS from max mass

Soft Nuclear Matter + CSS(c2

QM = 1)

2.0M๏ 2 . 3 M

๏

2 . 2 M๏

B A

2.1M๏

C D

Δε/εtrans

0.2 0.4 0.6 0.8 1 1.2

ptrans/εtrans

0.1 0.2 0.3 0.4 0.5

• Max mass data constrains QM EoS but does not rule out generic QM

Dependence of max mass on c2

QM Soft NM + CSS(c2

QM = 1/3)

1.5M๏ 1.6M๏ 1.8M๏ 2 . 1 M

๏

2.0M๏

B A C D

Δε/εtrans

0.2 0.4 0.6 0.8 1 1.2

ptrans/εtrans

0.05 0.1 0.15 0.2 0.25 0.3

Soft NM + CSS(c2

QM = 1)

2.0M๏ 2.3M๏ 2.2M๏

B A

2.1M๏

C D

Δε/εtrans

0.2 0.4 0.6 0.8 1 1.2

ptrans/εtrans

0.1 0.2 0.3 0.4 0.5

• For soft NM EoS, need c2

QM 0.4 to get 2 M⊙ stars

Quark matter EoS Summary

◮ CSS (Constant Speed of Sound) is a generic parameterization of the

EoS close to a sharp first-order transition to quark matter.

◮ Any specific model of quark matter with such a transition

corresponds to particular values of the CSS parameters

(ptrans/εtrans, ∆ε/εtrans, c2

QM).

Its predictions for hybrid star branches then follow from the generic CSS phase diagram.

◮ Existence of 2M⊙ neutron star → constraint on CSS parameters .

For soft NM we need c2

QM 0.4

(c2

QM = 1/3 for free quarks). ◮ More measurements of M(R) would tell us more about the EoS of

nuclear/quark matter. If necessary we could enlarge CSS to allow for density-dependent speed of sound.

r-modes and gravitational spin-down

An r-mode is a quadrupole flow that emits gravitational radiation. It becomes unstable (i.e. arises spon- taneously) when a star spins fast enough, and if the shear and bulk viscosity are low enough.

Side view Polar view

mode pattern star

The unstable r-mode can spin the star down very quickly, in a few days if the amplitude is large enough

(Andersson gr-qc/9706075; Friedman and Morsink gr-qc/9706073; Lindblom astro-ph/0101136).

neutron star spins quickly ⇒ some interior physics damps the r-modes

r-mode instability region for nuclear matter

Ω freq Spin

stabilizes stabilizes

T Temperature

bulk viscosity shear viscosity r−modes r−modes

unstable r−modes

Shear viscosity grows at low T (long mean free paths). Bulk viscosity has a resonant peak when beta equilibration rate matches r-mode frequency

• Instability region depends on viscosity of star’s interior.
• Behavior of stars inside instability region depends on

saturation amplitude of r-mode.

Evolution of r-mode amplitude α

dα dt = α(|γG| − γV ) γG =

1 τG = grav radiation rate (< 0)

γV =

1 τV = r-mode dissipation rate

dΩ dt = −2Q γV α2 Ω Q ≈ 0.1 for typical star dT dt = − 1

CV (Lν − PV )

Lν = neutrino emission PV = power from dissipation R-mode is unstable when |γG(Ω)| > γV (T) at infinitesimal α. R-mode saturates when γV (α) rises with α until γV (T, αsat) = γG (⇒ PV = PG) In general, αsat(T, Ω) is an unknown function determined by microscopic and astrophysical damping mechanisms.

R-modes and young neutron stars

Αsat1 Αsat104

107 108 109 1010 1011 0.0 0.2 0.4 0.6 0.8 1.0

T K K

Young pulsar cools into instability region R-mode quickly saturates Star spins down along “heating=cooling” line Star exits instability region at Ω ∼ 50 Hz, indp of cooling model

(Alford, Schwenzer arXiv:1210.6091)

Could r-modes explain young pulsar’s slow spin?

Crab

Αsat1 Αsat104

Vela J05376910

1 5 10 50 100 500 1000 1011 109 107

f Hz dfdt s2

r-modes with αsat ∼ 10−2 to 10−1 could explain slow rotation of young pulsars ( a few thousand years old) J0537-6910 is 4000 years old

(Alford, Schwenzer arXiv:1210.6091)

How quickly r-modes spin down pulsars

Αsat1 Αsat104

1010 105 1 105 0.0 0.2 0.4 0.6 0.8 1.0

t y K

For αsat in the range 0.01 to 0.1, spindown is complete in 20,000 to 500 years.

(Alford, Schwenzer arXiv:1210.6091)

GW from r-mode spindown of young pulsars

Known young pulsars. For given age t, h0 is indp of current freq ν, since if Ω = 2πν is higher, spindown would be faster, so αsat must be smaller to ensure we get to freq Ω in time t. Several known sources would be detected by advanced LIGO if they are mainly spinning down via r-modes.

Gravitational wave emission of young sources

• Advanced LIGO will become operational soon …
• Since r-mode emission can quantitively explain the low rotation

frequencies of observed pulsars (which spin by now too slow to emit GWs), very young sources are promising targets

SN 1987A SN 1957D J0537-6910 G1.9+0.3 Cas A 100 1000 500 200 300 150 1500 700 10-27 10-26 10-25 10-24 10-23 n @HzD h0 known timing data advanced LIGO HNS-opt.L HstandardL unknown timing LIGO 100 1000 500 200 300 150 1500 700 10-27 10-26 10-25 10-24 10-23 100 101 102 103 104 105 106 107 n @HzD h0 t@yD

Several potential sources in reach of aLigo

r-modes and old pulsars

Above curves, r-modes go unstable and spin down the star

J04374715

• viscous

damping hadronic matter Ekman layer interacting quark matter 104 105 106 107 108 109 1010 200 400 600 800 1000

T K f Hz

Data for accreting pulsars in binary systems (LMXBs) vs instability curves for nuclear and hybrid stars. Possibilities:

• additional damping

(e.g. quark matter)

• r-mode spindown is very

slow (small αsat)

(Alford, Schwenzer, arXiv:1310.3524 Haskell, Degenaar, Ho, arXiv:1201.2101)

Spindown via r-modes of an old neutron star

• steady state curve hc,

along which heating equals cooling boundary of the instability region slow accretion spinup slow rmode spindown cooling rapid

A B C D E F

min f

logT

• Steady-state spindown

curve is determined by amplitude αsat at which r-mode saturates. This determines final spin frequency Ωf . Stars with Ω < Ωf are not undergoing r-mode spindown.

r-mode spindown trajectories

• Αsat1010

Αsat105 Α

s a t

• 1

106 107 108 109 1010 100 200 300 400 500 600 700

T K f Hz

(Alford, Schwenzer, arXiv:1310.3524)

Explanations: 1) Instability boundary is wrong (additional damping). 2) Many neutron stars (ms pulsars and LMXBs) are stuck in the instability region, undergoing r-mode spindown with low saturation amplitude

• αsat ∼ 10−7
• T 107 K (r-mode

heating)

• they are emitting grav

waves

Gravitational waves from old ms-pulsars

• In addition to the standard

case of deformations 
 r-modes are a promising continuous GW-source

• But, the r-mode saturation

mechanism depends weakly

• n source properties …

★ novel universal spindown

limit for the GW signal ➡ Millisecond pulsars are below the aLigo sensitivity ✓ However they should be detectable with further improvements or 


• 3. generation detectors

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Gravitational wave frequency n @HzD Strain sensitivity h0

standard spindown limits universal spindown limits

mode coupling const model Aasi, et. al., 
 arXiv:1309.4027 Alford & Schwenzer, arXiv:1403.7500

(universal spindown limit)

“R-mode temperatures“

• The connection between the 


spindown curves allows to
 determine the R-mode temperature 


• f a star with saturated r-mode 

• scillations (tiny r-mode scenario)


for given timing data


• Independent of the 


saturation mechanism ...
 but depends on the cooling

• These are only upper bounds since 


the observed spindown rate can also stem from electromagnetic radiation ★ Measurements of temperatures of fast pulsars would allow us to test if saturated tiny r-modes can be present!

Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë Ë ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï Ï ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨

105 2â105 3â105 5â105 106 2â106 100 200 300 400 500 600 700

T• @KD f @HzD

Trm =

• IΩ ˙

Ω/

• 3ˆ

L 1/θ

hadronic 
 Modified Urca hadronic 
 direct Urca Alford & Schwenzer, arXiv:1310.3524

R-modes Summary

◮ r-modes are sensitive to viscosity and other damping characteristics

• f interior of star

◮ Mystery: There are stars inside the instability region for standard

“nuclear matter with viscous damping” model.

◮ Possible explanations:

◮

Microphysical extra damping (e.g. quark matter)

◮

Astrophysical extra damping (some currently unknown mechanism in a nuclear matter star)

◮

“tiny r-mode” = very low saturation amplitude

R-modes prospects

◮ a-LIGO will tell us whether some young neutron stars are spinning

down via r-modes

◮ Better temperature measurements of ms pulsars will tell us whether

they are inside the simple nuclear-viscous instability region.

◮ If they are inside, this tells us what value of αsat is required for

compatibility with the simple nuclear-viscous model.

◮ If we also know their ˙

Ω, we can see if they being heated by r-modes (T∞ ∼ 105 to 106 K).

◮ If pulsars with f 300 Hz are outside (too cool) this would require

amazingly low αsat 10−8 to be compatible with the simple nuclear-viscous model

◮ Now that we have calculations of r-mode spindown as a function of

general (generic power law) microphysical properties, let’s start surveying all known phases of dense matter for their spindown predictions

◮ Additional astrophysical damping could save simple nuclear-viscous

model; what other mechanisms could there be?

How will we identify hybrid stars?

EoS : density discontinuity at nuclear/quark transition leads to connected and/or disconnected branches in M(R). We need:

◮ better measurements of M and R ◮ theoretical constraints on basic properties of QM EoS

(ptrans/εtrans, ∆ε/εtrans, c2

QM) ◮ knowledge of nuclear matter EoS

Spindown : extra damping in some forms of quark matter can explain current observations, but other scenarios (astrophysical extra damping; r-modes with tiny amplitude) have not been ruled out. We need:

◮ Better theoretical understanding of r-mode damping and saturation

mechanisms

◮ Better temperature measurements (ideally, of ms pulsars too) ◮ Detect grav waves from old pulsars (beyond advanced LIGO) or

very young neutron stars (advanced LIGO)

Constraints on QM EoS from max mass

QM + Soft Nuclear Matter

2 . 3 M

๏

2 . 1 M๏ 2.0M๏ ntrans=2.0n0 (ptrans/εtrans=0.04) ntrans=4.0n0 (ptrans/εtrans=0.2) 2.2M๏ 2.0M๏

cQM

2

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Δε/εtrans = λ-1 0.2 0.4 0.6 0.8 1

QM + Hard Nuclear Matter

2.4M๏ 2.2M๏ 2.0M๏ ntrans=1.5n0 (ptrans/εtrans=0.1) ntrans=2.0n0 (ptrans/εtrans=0.17) 2.4M๏ 2.2M

๏

2.0M๏

cQM

2

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Δε/εtrans = λ-1 0.25 0.5 0.75 1 1.25 1.5

Alford, Han, Prakash, arXiv:1302.4732; Zdunik, Haensel, arXiv:1211.1231